﻿ Interpreting results: Coefficent of Variation

# Interpreting results: Coefficent of Variation

The coefficient of variation (CV), also known as “relative variability”, equals the standard deviation divided by the mean. It can be expressed either as a fraction or a percent.

What is the advantage of reporting CV? The only advantage is that it lets you compare the scatter of variables expressed in different units. It wouldn't make sense to compare the SD of blood pressure with the SD of pulse rate, but it might make sense to compare the two CV values.

Notes:

It only makes sense to report CV for variables, such as mass or enzyme activity, where “0.0” is defined to really mean zero. A weight of zero means no weight. An enzyme activity of zero means no enzyme activity. These are called ratio variables. It can be helpful to express variation of ratio variables (weights or enzyme activities...) as the CV. In contrast, a temperature of “0.0” does not mean zero temperature (unless measured in degrees Kelvin), so it would be meaningless to report a CV of values expressed as degrees C.

It never makes sense to calculate the CV of a variable expressed as a logarithm because the definition of zero is arbitrary. The logarithm of 1 equals 0, so the log will equal zero whenever the actual value equals 1. By changing units, you'll redefine 1.0 in the original scale, so redefine zero on the log scale, and so redefine the CV. The CV of a logarithm is, therefore, meaningless. For example, it makes no sense to compute the CV of a set of pH values. pH is measured on a log scale (it is the negative logarithm of the concentration of hydrogen ions). A pH of 0.0 does not mean 'no pH', and certainly doesn't mean 'no acidity' (quite the opposite). Therefore it makes no sense to compute the CV of pH.

When computing the CV, Prism computes the SD as the sample SD (using n-1 as the denominator) not the population SD (using n in the denominator).